Vector quaternionic spaces: geometry and classification

Summary: "The notion of a vector quaternionic (Q) space of general kind is introduced. Its main geometric characteristics, namely, metric, connection, curvature, torsion and non-metricity, are considered in local coordinates as well as in the associated tangent space with the help of differential forms. Two types of curvature and torsion constituents, affine and quaternionic, are distinguished, and a classification scheme for Q-space families is given, based on the presence, absence or compensatory properties of these characteristics or their parts. Altogether 13 different Q-space models are presented in a reduction procedure from general to quasi-Euclidean flat geometry."